## New kick-ass low discrepancy quasirandom sequence

**category:**general [glöplog]

Check this guys:

http://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequence s/

Better than Sobol, ultra easy to compute

http://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequence s/

Better than Sobol, ultra easy to compute

7

Nice!

... Oh my, what kind of crazy thing are you working on nowadays to be looking into this?

... Oh my, what kind of crazy thing are you working on nowadays to be looking into this?

Oh, it appeared on my Twitter feed and it is super useful for raytracing

That one is pretty cool and super trivial to implement.

TL;DR (for those who don't want to click links):

The 2D variant basically boils down to:

where i is the integer index of the sample and P is the Plastic Constant.

While this seems a pretty nice sequence for adaptive sampling, keep in mind that you can find better ones if you know the number of samples beforehand.

TL;DR (for those who don't want to click links):

The 2D variant basically boils down to:

**Code:**

` float2 sampleCoordinate = frac(i * float2(1.0/P, 1.0/(P*P)); `

where i is the integer index of the sample and P is the Plastic Constant.

While this seems a pretty nice sequence for adaptive sampling, keep in mind that you can find better ones if you know the number of samples beforehand.

He didn't compare to scrambled versions of the sequences or lattices/lattice sequences, which would make more sense for the 2D case, but still looks very interesting!

useful :)

Nice =) Now someone please connect this (mathematically) to my plane (fractal) filling cycle, where i visit each pixel exactly ONCE - implying a full green image in the "covering" section of the article - and then startover. I did some tests that imply the underlying random sequence is indeed very good, but have no proof yet.

Description

Tiny Intro Example

**Quote:**

Currently, i

dont't know exactly what "magic numbers" produce stable

plane filling cycles, how they are connected to the

branching criteria, or how to find them, other than by

trying. I'll leave that for later - or for the

mathemagicians amongst us ;)

Description

Tiny Intro Example

Just did some tests with this new sequence: Unfortunately it sucks for higher dimensions, as for example most low dimensional projections there show the same old stripes as most lattice based constructions do. So nothing to gain there. :/

And actually, as he points out himself, for d=1 & d=2, the sequence is already well known, plus IMHO the construction of the sequence is very similar to lattices in Korobov form, except that he uses irrational numbers instead of integers.

What i want to do next is to check 4 and 5D problems (like AO, sampling a set of area lights or camera DOF, note that the other 2 dimensions come from sampling the screen/pixel), cause that might actually work pretty well.

And actually, as he points out himself, for d=1 & d=2, the sequence is already well known, plus IMHO the construction of the sequence is very similar to lattices in Korobov form, except that he uses irrational numbers instead of integers.

What i want to do next is to check 4 and 5D problems (like AO, sampling a set of area lights or camera DOF, note that the other 2 dimensions come from sampling the screen/pixel), cause that might actually work pretty well.